313   two Turing machine by ``shifting'' the states of one by an appropriate

   313   two Turing machine by ``shifting'' the states of one by an appropriate

   314   amount to a higher segment.

   314   amount to a higher segment.

   315 

   315 

   316   An \emph{instruction} @{term i} of a Turing machine is a pair consisting of a

   316   An \emph{instruction} @{term i} of a Turing machine is a pair consisting of a

   317   natural number (the next state) and an action. A \emph{program} @{term p} of a Turing

   317   natural number (the next state) and an action. A \emph{program} @{term p} of a Turing

   319   and the cell being read by the read-write unit, we need to fetch

   327   and the cell being read by the read-write unit, we need to fetch

   320   the corresponding instruction from the program. For this we define 

   328   the corresponding instruction from the program. For this we define 

   321   the function @{term fetch}

   329   the function @{term fetch}

   322  

   330  

   323   \begin{center}

   331   \begin{center}

   423   which looks up the content of register $R$; if $R$

   431   which looks up the content of register $R$; if $R$

   424   is not in this list, then we return 0. Similarly we

   432   is not in this list, then we return 0. Similarly we

   425   have a setting function, written @{term "abc_lm_s m R\<iota> n"}, which

   433   have a setting function, written @{term "abc_lm_s m R\<iota> n"}, which

   426   sets the value of $R$ to $n$, and if $R$ was not yet in $m$

   434   sets the value of $R$ to $n$, and if $R$ was not yet in $m$

   427   it pads it approriately with 0s.

   435   it pads it approriately with 0s.

   428 *}

   439 *}

   429 

   440 

   430 

   441 

   431 section {* Recursive Functions *}

   442 section {* Recursive Functions *}

   432 

   443